Answers for Weekly Challenge 2 Challenge 1 (i) The key to calculating the breakeven point is to determine the contribution per unit. Contribution point = $120 ($22 + $36 + $14) = $48 Fixed overhead Breakeven point = $12 2,000 = 500 units = $48 (ii) Margin of safety = budgeted sales breakeven point = 2,200 500 = 1,700 units (or 1,700/2,200 100 %) = 77 % (iii) Once breakeven point has been reached, all of the contribution goes towards profits because all of the fixed costs have been covered. Budgeted profit = 1,700 units margin of safety $48 contribution per unit = $81,600 (iv) To achieve the desired level of profit, sufficient units must be sold to earn a contribution which covers the fixed costs and leaves the desired profit for the month. Fixed overhead + desired profit Number of sales units required = ($12 2,000) + $96,000 = $48 = 2,500 units
(v) is calculated as $120 $72 sum of variable costs = $48. Contribution to sales ratio = Sales revenue per unit $48 = $120 = 40% (iv) Breakeven revenue can be calculated in two ways. Monthly fixed costs B.E.R = Contribution to sales ratio $12 2,000 units = 40% = $60,000 This could also have been calculated as Breakeven Point 500 units x Selling price $120 = $60,000 Challenge 2 a) Break Even Point = $(100 56) = $44 $44 C/S ratio = = = 0.44 Selling price per unit $100 Breakeven point in terms numbers of units sold Fixed costs =
= $220,000 = 5,000 units $44 Breakeven point in terms of sales revenue Fixed costs = C/S ratio $220,000 = = $500,000 units 0.44 (Proof: breakeven units selling price per unit = 5,000 $100 = $500,000) (b) Margin of safety (as a % of Budgeted sales) = Budgeted sales Break-even sales 100% Budgeted sales 7,500 5,000 = 100% 7,500 = 33.33% Challenge 3 Firstly we need to calculate the breakeven sales revenue. Because we haven't been given any information on units, we must have to use the contribution sales revenue technique: Total contribution (450 220) C/S ratio = = Total sales revenue 450 = 0.511 (or 51.1%)
Fixed costs Breakeven point (in terms of sales revenue) = C/S ratio Breakeven point $160,000 (in terms of sales revenue) = 0.511 Breakeven point (in terms of sales revenue) = $313,000 Now that we know the break-even position we can calculate the margin of safety (this is what is required in the second element of the question). Margin of safety Budgeted sales Breakeven sales (as a % of = 100% budgeted sales) Budgeted sales Margin of safety 450 313 (as a % of = 100% budgeted sales) 450 = 0.3044 (or 30.44%) This tells us that for the company to fall into a loss making position its sales next year would have to fall by over 30.44% from their current position. Challenge 4 (a) First calculate the current contribution per unit. $000 $000 Sales revenue 288 Direct materials 54 Direct wages 72 Variable production overhead 18 Variable administration etc. 27 171 Contribution 117 ($117,000/9,000 units) $13
Now you can use the formula to calculate the breakeven point. Breakeven point = Fixed costs $42,000 + $ 36,000 = = 6,000 units $13 (b) Alternative (i) Budgeted contribution per unit $13 Reduction in selling price ($32 $28) $4 Revised contribution per unit $9 Revised breakeven point = $78,000/$9 8,667 units Revised sales volume = 9,000 (90/75) 10,800 units Revised contribution = 10,800 $9 $97,200 Less fixed costs $78,000 Revised profit $19,200 Alternative (ii) Budgeted contribution per unit $13.00 Reduction in selling price (15% $32) $4.80 Revised contribution per unit $8.20 $78,000 + $5,000 10,122 Units Revised breakeven point = $8.20 Revised sales volume = 9,000 units (100/75) 12,000 Units Revised contribution = 12,000 $8.20 $98,400 Less fixed costs $83,000 Revised profit $15,400
Neither of the two alternative proposals is worthwhile. They both result in lower forecast profits. In addition, they will both increase the breakeven point and will therefore increase the risk associated with the company s operations. (c) This exercise has shown you how an understanding of cost behaviour patterns and the manipulation of contribution can enable the rapid evaluation of the financial effects of a proposal. We can now expand it to demonstrate another aspect of the application of CVP analysis to short-term decision-making. Once again, the key is the required contribution. This time the contribution must be sufficient to cover both the fixed costs and the required profit. If we then divide this amount by the contribution earned from each unit, we can determine the required sales volume. Fixed costs + required profit Required sales = ($42,000 + $36,000 + $45,500) = = 9,500 units $13 Challenge 5 Step 1: Determine the Maximum Sales Platinum, Gold & Silver are not potential limiting factors for the purpose of this analysis as they do not affect the production of other products unlike steel and labor which are required in the production of all watches. However, we need to ensure that any shortage in the availability of Platinum, Gold or Silver is accounted for when calculating the resource requirements of potential limiting factors (i.e. steel and labor) in Step 2 based on the maximum sales. Factor Available Units Maximum Output Sales Demand Maximum Sales A B Lower of A & B Platinum 200 KG 1100 units (W1) 1000 Units 1000 Units Gold 300 KG 2000 units (W2) 2000 Units 2000 Units Silver 200 KG 2000 units (W3) 2500 Units 2000 Units W1 : Platinum Watches: 220 KG / 0.2 KG* = 1100 units *200 grams = 0.2 KG W2: Gold Watches: 300 KG / 0.15 KG* = 2000 units *150 grams = 0.15 KG W3: Silver Watches: 200 KG / 0.10 KG* = 2000 units *100 grams = 0.10 KG
Step 2: Determine the Limiting Factor Factor Available Units Required units Shortfall Steel 2200 KG 2500 KG (W1) Yes Labor 200,000 hours 190,000 hrs (W2) No Steel is the limiting factor. W1: Steel Units required to produce maximum sales units Platinum: 500 grams x 1000 units = 500 KG Gold: 400 grams x 2000 units = 800 KG Silver: 600 grams x 2000 units = 1200 KG Total Steel Units: 2500 KG W2: Labor hours required to produce maximum sales units Platinum: 50 hours x 1000 units = 50,000 hours Gold: 40 hours x 2000 units = 80,000 hours Silver: 30 hours x 2000 units = 60,000 hours Total Labour hours: 190,000 hours Step 3: Calculate the Contribution Per Unit of each product Product Revenue Variable cost Contribution per Unit A B A-B Platinum $10,000 $6,300 $4,700 Gold $8,000 $4,980 $3,020 Silver $5,000 $2,160 $2,840 Step 4: Calculate the Contribution Per Unit of Limiting Factor of each product Product Contriubtion per Unit Stainless Steel per Contribution of products Unit per unit of limiting factor A B A / B Platinum $4,700 500 grams $9.4 per gram Gold $3,020 400 grams $7.55 per gram Silver $2,840 600 grams $4.73 per gram Step 5: Rank products in their order of priority in the production plan Product Contribution of Products per unit of limiting factor Rank Platinum $9.40 per gram 1 Gold $7.55 per gram 2 Silver $4.73 per gram 3 Since Platinum Watches earn the highest contribution for every gram of stainless steel used, it is given first priority in the production plan followed by Gold and Silver Watches. Step 6: Calculate the production quantities Product Rank Steel Units Steel Units Units to be Available Required Produced Platinum 1 2200 KG 500 KG (W3) 1000 Gold 2 1700 KG (W1) 800 KG (W4) 2000 Silver 3 900 KG (W2) 900 KG (W4) 1500 (W5) 1000 Platinum Watches, 2000 Gold Watches and 1500 Silver Watches should be produced to maximize profit. Platinum and gold watches can be produced up to the level of their maximum sales. However, only 1500 Silver watches can be produced from the steel units available after the production of platinum and gold watches. W1: 2200 KG - 500 KG = 1700 KG W2: 1700 KG - 800 KG = 900 KG W3: 1000 units x 500 grams per unit = 500 KG W4: 2000 units x 400 grams per unit = 800 KG W5: 900 KG / 0.6 KG* = 1500 units *600 grams = 0.6 KG